Title
An Application of Kleene's Fixed Point Theorem to Dynamic Programming: A Note
Abstract
In this note, we show that the least fixed point of the Bellman operator in a certain set can be computed by value iteration whether or not the fixed point is the value function. As an application, we show one of the main results of Kamihigashi (2014, "Elementary results on solutions to the Bellman equation of dynamic programming:existence, uniqueness, and convergence," Economic Theory 56, 251-273) with a simpler proof.
Keywords
Dynamic programming, Bellman equation, Value function,Fixed point
JEL Classification
C61
Inquiries
Takashi KAMIHIGASHI
Research Institute for Economics and Business Administration,
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: +81-78-803-7036
FAX: +81-78-803-7059
Kevin REFFETT
Department of Economics, Arizona State University
Masayuki YAO
Department of Economics, Keio University
Research Institute for Economics and Business Administration,
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501 Japan
Phone: +81-78-803-7036
FAX: +81-78-803-7059
Kevin REFFETT
Department of Economics, Arizona State University
Masayuki YAO
Department of Economics, Keio University